Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int32_t main() {
  long long n;
  cin >> n;
  vector<long long> a;
  long long num = 1, diff = 2;
  while (num <= n) {
    a.push_back(num);
    num = num + diff;
    diff++;
  }
  for (long long i = 0; i < a.size(); i++) {
    long long lo = i, hi = a.size() - 1;
    while (lo <= hi) {
      long long mid = lo + (hi - lo) / 2;
      if (a[mid] + a[i] == n) {
        cout << "YES\n";
        return 0;
      } else if (a[mid] + a[i] > n) {
        hi = mid - 1;
      } else {
        lo = mid + 1;
      }
    }
  }
  cout << "NO\n";
  return 0;
}